Dual polarization radars send and receive electromagnetic waves with two polarizations as shown in FIG. 1. These polarizations can be orthogonal; for example, with horizontal and vertical polarizations. A dual polarization radar can measure differential propagation phase shift (ΦDp) between the two polarizations. The specific differential phase (Kdp), defined as the slope of the differential propagation phase shift (ΦDp) with respect to range, can be an important parameter for weather radar applications. Estimation of the specific differential phase can require computing the numerical derivative of range profiles of the differential propagation phase. The existence of possible phase wrapping, noise and/or statistical fluctuation in the differential propagation phase have made the evaluation of the specific differential phase an unstable numerical process.